A boy measured the length and breadth of rectangular lawn as 96.6m and 40.3m respectively instead of 60m and 40m.what is the percentage error in his calculation of the perimeter of the lawn?
perimeter 1 = 2(96.6) + 2(40.3) = ?
Perimeter 2 = ?
(1-2)/2 = ?
Change to percentage
It's the actual error divided by the true amount:
96.6 vs 60 for the length? Gotta be a typo of major proportions. I shall assume you meant 60.6
((60.6+40.3) - (60+40))/(60+40) = (100.9 - 100)/100 = 0.9/100 or 0.9%
yeah, I know there's factor of 2 missing, but it appears everywhere, so it cancels out.
To calculate the percentage error in the calculation of the perimeter of the lawn, we first need to find the actual and measured perimeters.
Step 1: Calculate the actual perimeter.
The actual perimeter of a rectangle can be found using the formula:
Perimeter = 2 × (Length + Breadth)
Given that the actual length of the lawn is 60m and the actual breadth is 40m:
Actual Perimeter = 2 × (60 + 40)
Actual Perimeter = 2 × 100
Actual Perimeter = 200m
Step 2: Calculate the measured perimeter.
The measured perimeter of a rectangle can also be found using the formula:
Measured Perimeter = 2 × (Measured Length + Measured Breadth)
Given that the measured length is 96.6m and the measured breadth is 40.3m:
Measured Perimeter = 2 × (96.6 + 40.3)
Measured Perimeter = 2 × 136.9
Measured Perimeter = 273.8m
Step 3: Calculate the percentage error.
Percentage Error = [(Measured Perimeter - Actual Perimeter) / Actual Perimeter] × 100
Percentage Error = [(273.8 - 200) / 200] × 100
Percentage Error = (73.8 / 200) × 100
Percentage Error = 0.369 × 100
Percentage Error = 36.9%
Therefore, the percentage error in the boy's calculation of the perimeter of the lawn is 36.9%.
To calculate the percentage error in the boy's calculation of the perimeter of the lawn, we need to compare the actual perimeter with the perimeter calculated using the incorrect measurements.
The actual length of the rectangular lawn is 60m, and the actual breadth is 40m. So, the actual perimeter can be calculated as:
Actual Perimeter = 2 * (Length + Breadth)
= 2 * (60m + 40m)
= 2 * 100m
= 200m
The boy measured the length as 96.6m and the breadth as 40.3m. Using these measurements, the perimeter he calculated can be obtained as:
Calculated Perimeter = 2 * (Measured Length + Measured Breadth)
= 2 * (96.6m + 40.3m)
= 2 * 136.9m
= 273.8m
Now, to find the percentage error, we use the formula:
Percentage Error = (|Actual Value − Measured Value| ÷ Actual Value) × 100
In this case, the actual perimeter is 200m, and the measured perimeter is 273.8m. Plugging these values into the formula, we get:
Percentage Error = (|200m - 273.8m| ÷ 200m) × 100
= (73.8m ÷ 200m) × 100
= 0.369 × 100
= 36.9%
Therefore, the percentage error in the boy's calculation of the perimeter of the lawn is 36.9%.